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Synonyms for Unresolvable (same or very similar meaning)

WordNet sense 1 (not easily solved):
insolvable, unsolvable, unsoluble

WordNet sense 2 (admitting of no solution or explanation):
insoluble

WordNet sense 3 (not permitting extrication; incapable of being disentangled or untied):
inextricable


From the ODE community, based on WordNetadd/edit